From the test statistic calculated, reject 1 that SSE Index time series has a unit root.
, there is sufficient evidence showing
Similarly, the test statistic is calculated for S&P 500 Index:
Test Statistic: -0.21946
Again, reject 1
, there is sufficient evidence supporting that S&P 500 possess a
unit root.
To conclude, both hypotheses of 0 cannot be rejected at any significance level, therefore the original data do follow a random walk process, which are both I (1) time series.
1.1Durbin Watson test for Cointegration
∑ ( =2
) 2
− −1
=
2
∑ =1
Numerator: 0.821091 Denominator: 16.24786
d=0.050535 Finally, we need to use the CRDW critical value table to test the statistic calculated.
Number of variables (incl. )
Number of observations
50 100
200
2
0.72 0.89 1.05 1.19
0.38 0.48 0.58 0.68
0.20 0.25 0.30 0.35
3 4 5
Table.3: 5% critical values CRDW tests for no
cointegration
In our sample there are 2 variables and totally 164 observations therefore, from the table, the critical values are between 0.38 and 0.20, however, the 𝒹 we’ve calculated (0.050535) is way lower which strongly suggests that there is no cointegration between these two time series.
5. Conclusion
The object of this paper was to examine long-term cointegration between S&P Index and SSE Index for the period December 2001 to April 2015. We first use the Dickey Fuller test to examine the order of integration of each time series as it is a necessary step for setting up an econometric model and do inference later on. The test has the null hypothesis that the series is (1) which
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